Question

a water footprint is a measure of the appropriation of fresh water. the per capita water footprint (in mega gallons) in a certain country for a recent year can be approximated by a normal distribution, as shown in the figure. (a) what water footprint represents the 80th percentile? (b) what water footprint represents the 29th percentile? (c) what water footprint represents (a) the water footprint that represents the 80th percentile is 4.12 mgal (round to two decimal places as needed.) (b) the water footprint that represents the 29th percentile is mgal (round to two decimal places as needed.)

Explanation:

Step1: Recall z - score formula

The formula for a value $x$ in a normal distribution is $x=\mu + z\sigma$, where $\mu$ is the mean, $z$ is the z - score, and $\sigma$ is the standard deviation. Here, $\mu = 1.68$ Mgal and $\sigma=2.9$ Mgal.

Step2: Find z - score for 29th percentile

We look up the z - score corresponding to a cumulative probability of 0.29 in the standard normal distribution table. The z - score $z_{0.29}\approx - 0.55$.

Step3: Calculate the water footprint

Substitute $\mu = 1.68$, $z=- 0.55$, and $\sigma = 2.9$ into the formula $x=\mu+z\sigma$. So $x=1.68+( - 0.55)\times2.9=1.68 - 1.595 = 0.085\approx0.09$ Mgal.

Answer:

0.09 Mgal